This multi-center, randomized, double-blind, placebo-controlled parallel-group study will evaluate the effect of gantenerumab (RO4909832) on cognition and functioning and the safety and pharmacokinetics in participants with prodromal Alzheimer's Disease. Participants will be randomized to receive subcutaneous (SC) injections of either gantenerumab or placebo. Participants who consent to be part of the sub study will undergo positron emission tomography (PET) scanning to assess brain amyloid. The anticipated time on study treatment is 104 weeks, with an option for an additional 2 years of treatment.